本次共计算 1 个题目：每一题对 x 求 2 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数xsqrt(\frac{(x - 1)(x - 2)}{((x - 3)(x - 4))}) 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = xsqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( xsqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})\right)}{dx}\\=&sqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)}) + \frac{x((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))*\frac{1}{2}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\\=&sqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)}) - \frac{x^{4}}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{13x^{3}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{x^{2}}{(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{25x^{2}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{3x}{2(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{7x}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sqrt(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)}) - \frac{x^{4}}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{13x^{3}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{x^{2}}{(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{25x^{2}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{3x}{2(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{7x}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\right)}{dx}\\=&\frac{((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))*\frac{1}{2}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{(\frac{-2(2x - 7 + 0)}{(x^{2} - 7x + 12)^{3}})x^{4}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}})x^{4}}{(x^{2} - 7x + 12)^{2}} - \frac{4x^{3}}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{13(\frac{-2(2x - 7 + 0)}{(x^{2} - 7x + 12)^{3}})x^{3}}{2(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{13(\frac{\frac{-1}{2}((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}})x^{3}}{2(x^{2} - 7x + 12)^{2}} + \frac{13*3x^{2}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}})x^{2}}{(x^{2} - 7x + 12)} + \frac{2x}{(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{25(\frac{-2(2x - 7 + 0)}{(x^{2} - 7x + 12)^{3}})x^{2}}{2(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{25(\frac{\frac{-1}{2}((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}})x^{2}}{2(x^{2} - 7x + 12)^{2}} - \frac{25*2x}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x}{2(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}})x}{2(x^{2} - 7x + 12)} - \frac{3}{2(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{7(\frac{-2(2x - 7 + 0)}{(x^{2} - 7x + 12)^{3}})x}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{7(\frac{\frac{-1}{2}((\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x^{2} + \frac{2x}{(x^{2} - 7x + 12)} - 3(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}})x - \frac{3}{(x^{2} - 7x + 12)} + 2(\frac{-(2x - 7 + 0)}{(x^{2} - 7x + 12)^{2}}))}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}})x}{(x^{2} - 7x + 12)^{2}} + \frac{7}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\\=&\frac{-3x^{3}}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{33x^{2}}{2(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{x}{(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{x^{3}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{2}} - \frac{40x^{4}}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{4x^{5}}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{2x^{5}}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}} - \frac{16x^{4}}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}} + \frac{141x^{3}}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{x^{7}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} + \frac{13x^{6}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} + \frac{89x^{3}}{2(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}} - \frac{269x^{5}}{4(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} - \frac{203x^{2}}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{353x^{4}}{2(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} - \frac{4x^{3}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}(x^{2} - 7x + 12)^{2}} - \frac{989x^{3}}{4(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} - \frac{103x^{2}}{2(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}} + \frac{39x^{2}}{2(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}(x^{2} - 7x + 12)^{2}} + \frac{3x^{2}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{2}} - \frac{23x}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{2x}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}(x^{2} - 7x + 12)} - \frac{25x}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}(x^{2} - 7x + 12)^{2}} - \frac{9x}{4(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{2}} + \frac{21x}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}} + \frac{98x}{(x^{2} - 7x + 12)^{3}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} + \frac{175x^{2}}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} - \frac{49x}{(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{3}{2}}(x^{2} - 7x + 12)^{4}} + \frac{14}{(x^{2} - 7x + 12)^{2}(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}} - \frac{3}{(x^{2} - 7x + 12)(\frac{x^{2}}{(x^{2} - 7x + 12)} - \frac{3x}{(x^{2} - 7x + 12)} + \frac{2}{(x^{2} - 7x + 12)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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